A group of charter school advocates, business leaders, and legislators is pushing to abolish a state-imposed cap on the number of charter schools that can operate in Boston and other low-performing school districts, under legislation expected to be filed Friday on Beacon Hill.

The proposal is anticipated three years after the Legislature and Governor Deval Patrick decided to double the number of charter school seats in those districts. That change created the opportunity for about 5,000 additional students in Boston to attend charter schools.

But demand for seats has proved to be so robust that the state Board of Elementary and Secondary Education is expected to approve the final batch of new independently run charter schools next month for Boston, Holyoke, and Lawrence.

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If state law is not changed, no more charter schools will be allowed to open in those cities, even though waiting lists for charter schools across the state have grown to 45,000 students.

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“We have some of the best charter schools in the nation in Boston,” said Marc Kenen, executive ­director of the Massachusetts Charter Public School Association, one of the groups behind the legislation. “For the state not to allow more of these schools to open would be a shame.”

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The proposal would join a growing list of bills filed this week seeking to overhaul public education, making education one of the highest-profile issues that the Legislature is likely to confront this session.

Abolishing the charter school cap is just one aspect of the legislation, which is being sponsored by Senator Barry Finegold of Andover and Representative Russell Holmes of Mattapan, both Democrats.

“We do need to change the way we educate our kids, especially in urban areas,” said Finegold, who also represents Lawrence.

Patrick’s plan includes additional learning time in middle schools, extra state aid for local districts, and several measures that target early childhood and higher education. It makes no mention of abolishing charter school caps or providing superintendents more flexibility to overhaul schools, accord­ing to a summary released by the governor’s office.

A Patrick spokeswoman said Thursday that the governor looks forward to seeing the legislation once it has been filed.

Created under the 1993 Education Reform Act, the state’s 67 independently run charter schools are designed to provide innovative educational alternatives to traditional public schools because they ­operate with fewer restrictions from the state and almost always employ nonunion teachers.

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Many charter schools have among the best state standardized test scores.

“When something is working in such an important area as lifting the prosperity of low-income children, there is no rationale for restricting those practices,” said Paul Grogan, president of the Boston Foundation, a charitable organization pushing for the legislation.

But charter schools are not a silver bullet, and state officials have closed some because of poor performance.

Most school systems have long opposed the proliferation of charter schools because districts lose thousands of dollars in state aid for each student who chooses to attend a charter school. To help cushion that blow, the state limits the amount of a district’s budget that can go toward charter school ­tuition, thereby restricting the number of schools.

For more than a decade, no more than 9 percent of a district’s “net school spending” could pay for charter school tuition. But three years ago, the state increased that level to 18 percent in Boston and other low-performing districts, as part of an effort to double charter school enrollments in those areas.

Now, Boston, Holyoke, and Lawrence are already near those spending levels, which after this year will prevent opening additional charter schools.

Boston has 20 charter schools, and plans have been filed with the state for three additional schools to serve 1,000 students, while six existing charter schools are seeking to add 800 seats. The state will have to reject some of those proposals because of the cap.

“The inescapable conclusion is that we should not have a cap,” said Paul Sagan, executive vice president at Akamai and cochairman of Massachusetts Business Leaders for Charter Public Schools.

Matthew Wilder, a Boston School Department spokesman, declined to comment on abolishing the charter school cap, but expressed optimism that families will choose to stay in the system.

“We have been working hard in [the] district to improve the quality of schools,” Wilder said.

Holmes said he was motivated to file the legislation because too many students are still struggling in school, especially in a state that is often in the top on national standardized tests.

“It instills a lot of pride in me to say ‘Massachusetts is number one in the country,’ but I’m disappointed we are not doing better in my own neighborhood,” Holmes said.